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FE
Reference Handbook
9.4 V ersion for Computer-Based Testing
Copyright ©2013 by NCEES®. All rights reserved.
All NCEES material is copyrighted under the laws of the United States. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted in any form or by any means without the prior written permission of NCEES. Requests for permissions
should be addressed in writing to [email protected].
PO Box 1686
Clemson, SC 29633
800-250-3196
www.ncees.org
ISBN 978-1-932613-67-4
Printed in the United States of America
Fourth printing June 2016
Edition 9.4
PREFACE
About the Handbook
The Fundamentals of Engineering (FE) exam is computer-based, and the FE Reference Handbook is the only
resource material you may use during the exam. Reviewing it before exam day will help you become familiar
with the charts, formulas, tables, and other reference information provided. You won't be allowed to bring your
personal copy of the Handbook into the exam room. Instead, the computer-based exam will include a PDF
version of the Handbook for your use. No printed copies of the Handbook will be allowed in the exam room.
The PDF version of the FE Reference Handbook that you use on exam day will be very similar to the printed
version. Pages not needed to solve exam questions—such as the cover, introductory material, index, and exam
specifications—will not be included in the PDF version. In addition, NCEES will periodically revise and
update the Handbook, and each FE exam will be administered using the updated version.
The FE Reference Handbook does not contain all the information required to answer every question on the
exam. Basic theories, conversions, formulas, and definitions examinees are expected to know have not been
included. Special material required for the solution of a particular exam question will be included in the
question itself.
Updates on exam content and procedures
NCEES.org is our home on the web. Visit us there for updates on everything exam-related, including
specifications, exam-day policies, scoring, and practice tests. A PDF version of the FE Reference Handbook
similar to the one you will use on exam day is also available there.
Errata
To report errata in this book, send your correction using our chat feature on NCEES.org. We will also post
errata on the website. Examinees are not penalized for any errors in the Handbook that affect an exam
question.
CONTENTS
Units ...................................................................................................................1
Conversion Factors .............................................................................................2
Ethics ..................................................................................................................3
Safety ..................................................................................................................6
Mathematics .....................................................................................................22
Engineering Probability and Statistics .............................................................37
Chemistry .........................................................................................................54
Materials Science/Structure of Matter .............................................................60
Statics ...............................................................................................................67
Dynamics ..........................................................................................................72
Mechanics of Materials ....................................................................................80
Thermodynamics ..............................................................................................87
Fluid mechanics .............................................................................................103
Heat Transfer ...................................................................................................117
Instrumentation, Measurement, and Controls ................................................124
Engineering Economics .................................................................................131
Chemical Engineering ....................................................................................138
Civil Engineering ...........................................................................................146
Environmental Engineering ...........................................................................179
Electrical and Computer Engineering ............................................................200
Industrial and Systems Engineering ...............................................................228
Mechanical Engineering .................................................................................237
Index ...............................................................................................................251
Appendix: FE Exam Specifications ...............................................................257
UNITS
The FE exam and this handbook use both the metric system of units and the U.S. Customary System (USCS). In the USCS system of
units, both force and mass are called pounds. Therefore, one must distinguish the pound-force (lbf) from the pound-mass (lbm).
2 2
The pound-force is that force which accelerates one pound-mass at 32.174 ft/sec . Thus, 1 lbf = 32.174 lbm-ft/sec . The expression 32.174
2
lbm-ft/(lbf-sec ) is designated as gc and is used to resolve expressions involving both mass and force expressed as pounds. For instance, in
2
writing Newton's second law, the equation would be written as F = ma/gc, where F is in lbf, m in lbm, and a is in ft/sec .
2
Similar expressions exist for other quantities. Kinetic Energy, KE = mv /2gc, with KE in (ft-lbf); Potential Energy, PE = mgh/gc, with PE in
2 3
(ft-lbf); Fluid Pressure, p = ρgh/gc, with p in (lbf/ft ); Specific Weight, SW = ρg/gc, in (lbf/ft ); Shear Stress, τ = (µ/gc)(dv/dy), with shear
2
stress in (lbf/ft ). In all these examples, gc should be regarded as a force unit conversion factor. It is frequently not written explicitly in
engineering equations. However, its use is required to produce a consistent set of units.
2
Note that the force unit conversion factor gc [lbm-ft/(lbf-sec )] should not be confused with the local acceleration of gravity g, which
2 2 2 2
has different units (m/s or ft/sec ) and may be either its standard value (9.807 m/s or 32.174 ft/sec ) or some other local value.
If the problem is presented in USCS units, it may be necessary to use the constant gc in the equation to have a consistent set of units.
METRIC PREFIXES
COMMONLY USED EQUIVALENTS
Multiple Prefix Symbol
10–18 atto a
10–15 femto f 1 gallon of water weighs 8.34 lbf
10–12 pico p 1 cubic foot of water weighs 62.4 lbf
10–9 nano n 1 cubic inch of mercury weighs 0.491 lbf
10–6 micro µ
The mass of 1 cubic meter of water is 1,000 kilograms
10–3 milli m
1 mg/L is 8.34 lbf/Mgal
10–2 centi c
10–1 deci d
101 deka da
TEMPERATURE CONVERSIONS
102 hecto h
103 kilo k
106 mega M ºF = 1.8 (ºC) + 32
109 giga G ºC = (ºF – 32)/1.8
1012 tera T ºR = ºF + 459.69
1015 peta P K = ºC + 273.15
1018 exa E
IDEAL GAS CONSTANTS
The universal gas constant, designated as R in the table below, relates pressure, volume, temperature, and number of moles of an ideal
gas. When that universal constant, R, is divided by the molecular weight of the gas, the result, often designated as R, has units of energy
per degree per unit mass [kJ/(kg·K) or ft-lbf/(lbm-ºR)] and becomes characteristic of the particular gas. Some disciplines, notably
chemical engineering, often use the symbol R to refer to the universal gas constant R.
FUNDAMENTAL CONSTANTS
Quantity Symbol Value Units
−19
electron charge e 1.6022 × 10 C (coulombs)
Faraday constant F 96,485 coulombs/(mol)
gas constant metric R 8,314 J/(kmol·K)
gas constant metric R 8.314 kPa·m3/(kmol·K)
gas constant USCS R 1,545 ft-lbf/(lb mole-ºR)
R 0.08206 L-atm/(mole-K)
–11 3 2
gravitation−Newtonian constant G 6.673 × 10 m /(kg·s )
–11 2 2
gravitation−Newtonian constant G 6.673 × 10 N·m /kg
2
gravity acceleration (standard) metric g 9.807 m/s
2
gravity acceleration (standard) USCS g 32.174 ft/sec
molar volume (ideal gas), T = 273.15K, p = 101.3 kPa V 22,414 L/kmol
m
speed of light in vacuum c 299,792,000 m/s
–8 2 4
Stefan-Boltzmann constant σ 5.67 × 10 W/(m ·K )
1 UNITS
CONVERSION FACTORS
Multiply By To Obtain Multiply By To Obtain
acre 43,560 square feet (ft2) joule (J) 9.478 × 10–4 Btu
ampere-hr (A-hr) 3,600 coulomb (C) J 0.7376 ft-lbf
ångström (Å) 1 × 10–10 meter (m) J 1 newton·m (N·m)
atmosphere (atm) 76.0 cm, mercury (Hg) J/s 1 watt (W)
atm, std 29.92 in., mercury (Hg)
atm, std 14.70 lbf/in2 abs (psia) kilogram (kg) 2.205 pound (lbm)
atm, std 33.90 ft, water kgf 9.8066 newton (N)
atm, std 1.013 × 105 pascal (Pa) kilometer (km) 3,281 feet (ft)
km/hr 0.621 mph
bar 1 × 105 Pa kilopascal (kPa) 0.145 lbf/in2 (psi)
bar 0.987 atm kilowatt (kW) 1.341 horsepower (hp)
barrels–oil 42 gallons–oil kW 3,413 Btu/hr
Btu 1,055 joule (J) kW 737.6 (ft-lbf )/sec
Btu 2.928 × 10–4 kilowatt-hr (kWh) kW-hour (kWh) 3,413 Btu
Btu 778 ft-lbf kWh 1.341 hp-hr
Btu/hr 3.930 × 10–4 horsepower (hp) kWh 3.6 × 106 joule (J)
Btu/hr 0.293 watt (W) kip (K) 1,000 lbf
Btu/hr 0.216 ft-lbf/sec K 4,448 newton (N)
calorie (g-cal) 3.968 × 10–3 Btu liter (L) 61.02 in3
cal 1.560 × 10–6 hp-hr L 0.264 gal (U.S. Liq)
cal 4.186 joule (J) L 10–3 m3
cal/sec 4.184 watt (W) L/second (L/s) 2.119 ft3/min (cfm)
centimeter (cm) 3.281 × 10–2 foot (ft) L/s 15.85 gal (U.S.)/min (gpm)
cm 0.394 inch (in)
centipoise (cP) 0.001 pascal·sec (Pa·s) meter (m) 3.281 feet (ft)
centipoise (cP) 1 g/(m·s) m 1.094 yard
centipoise (cP) 2.419 lbm/hr-ft m/second (m/s) 196.8 feet/min (ft/min)
centistoke (cSt) 1 × 10–6 m2/sec (m2/s) mile (statute) 5,280 feet (ft)
cubic feet/second (cfs) 0.646317 million gallons/day (MGD) mile (statute) 1.609 kilometer (km)
cubic foot (ft3) 7.481 gallon mile/hour (mph) 88.0 ft/min (fpm)
cubic meters (m3) 1,000 liters mph 1.609 km/h
electronvolt (eV) 1.602 × 10–19 joule (J) mm of Hg 1.316 × 10–3 atm
mm of H O 9.678 × 10–5 atm
2
foot (ft) 30.48 cm
ft 0.3048 meter (m) newton (N) 0.225 lbf
ft-pound (ft-lbf) 1.285 × 10–3 Btu newton (N) 1 kg·m/s2
ft-lbf 3.766 × 10–7 kilowatt-hr (kWh) N·m 0.7376 ft-lbf
ft-lbf 0.324 calorie (g-cal) N·m 1 joule (J)
ft-lbf 1.356 joule (J)
pascal (Pa) 9.869 × 10–6 atmosphere (atm)
ft-lbf/sec 1.818 × 10–3 horsepower (hp) Pa 1 newton/m2 (N/m2)
Pa·sec (Pa·s) 10 poise (P)
gallon (U.S. Liq) 3.785 liter (L) pound (lbm, avdp) 0.454 kilogram (kg)
gallon (U.S. Liq) 0.134 ft3 lbf 4.448 N
gallons of water 8.3453 pounds of water lbf-ft 1.356 N·m
gamma (γ, Γ) 1 × 10–9 tesla (T) lbf/in2 (psi) 0.068 atm
gauss 1 × 10–4 T psi 2.307 ft of H O
gram (g) 2.205 × 10–3 pound (lbm) psi 2.036 in. of H2g
psi 6,895 Pa
hectare 1 × 104 square meters (m2)
hectare 2.47104 acres radian 180/π degree
horsepower (hp) 42.4 Btu/min
hp 745.7 watt (W) stokes 1 × 10–4 m2/s
hp 33,000 (ft-lbf)/min
hp 550 (ft-lbf)/sec therm 1 × 105 Btu
hp-hr 2,545 Btu ton (metric) 1,000 kilogram (kg)
hp-hr 1.98 × 106 ft-lbf ton (short) 2,000 pound (lb)
hp-hr 2.68 × 106 joule (J)
hp-hr 0.746 kWh watt (W) 3.413 Btu/hr
W 1.341 × 10–3 horsepower (hp)
inch (in.) 2.540 centimeter (cm) W 1 joule/s (J/s)
in. of Hg 0.0334 atm weber/m2 (Wb/m2) 10,000 gauss
in. of Hg 13.60 in. of H O
2
in. of H O 0.0361 lbf/in2 (psi)
2
in. of H O 0.002458 atm
2
2 CONVERSION FACTORS
ETHICS
CODES OF ETHICS No code can give immediate and mechanical answers to all
Engineering is considered to be a "profession" rather than an ethical and professional problems that an engineer may face.
"occupation" because of several important characteristics shared Creative problem solving is often called for in ethics, just as it is
with other recognized learned professions, law, medicine, and in other areas of engineering.
theology: special knowledge, special privileges, and special
responsibilities. Professions are based on a large knowledge base Model Rules, Section 240.15, Rules of Professional Conduct
requiring extensive training. Professional skills are important
To safeguard the health, safety, and welfare of the public and to
to the well-being of society. Professions are self-regulating,
maintain integrity and high standards of skill and practice in the
in that they control the training and evaluation processes that
engineering and surveying professions, the rules of professional
admit new persons to the field. Professionals have autonomy
conduct provided in this section shall be binding upon every
in the workplace; they are expected to utilize their independent
licensee and on all firms authorized to offer or perform
judgment in carrying out their professional responsibilities.
engineering or surveying services in this jurisdiction.
Finally, professions are regulated by ethical standards. (Harris,
A. Licensee's Obligation to the Public
C.E., M.S. Pritchard, & M.J. Rabins, Engineering Ethics:
1. Licensees shall be cognizant that their first and foremost
Concepts and Cases, Wadsworth Publishing company, pages
responsibility is to safeguard the health, safety, and
27–28, 1995.)
welfare of the public when performing services for
The expertise possessed by engineers is vitally important to clients and employers.
societal welfare. In order to serve society effectively, engineers 2. Licensees shall sign and seal only those plans, surveys,
must maintain a high level of technical competence. However, and other documents that conform to accepted
a high level of technical expertise without adherence to ethical engineering and surveying standards and that safeguard
guidelines is as much a threat to public welfare as is professional the health, safety, and welfare of the public.
incompetence. Therefore, engineers must also be guided by 3. Licensees shall notify their employer or client and
ethical principles. such other authority as may be appropriate when their
professional judgment is overruled under circumstances
The ethical principles governing the engineering profession are
in which the health, safety, or welfare of the public is
embodied in codes of ethics. Such codes have been adopted by
endangered.
state boards of registration, professional engineering societies,
4. Licensees shall, to the best of their knowledge, include
and even by some private industries. An example of one such
all relevant and pertinent information in an objective
code is the NCEES Rules of Professional Conduct, found in
and truthful manner within all professional documents,
Section 240 of the Model Rules and presented here. As part of
statements, and testimony.
his/her responsibility to the public, an engineer is responsible for
5. Licensees shall express a professional opinion publicly
knowing and abiding by the code. Additional rules of conduct
only when it is founded upon an adequate knowledge
are also included in the Model Rules.
of the facts and a competent evaluation of the subject
The three major sections of the Model Rules address (1)
matter.
Licensee's Obligation to the Public, (2) Licensee's Obligation
6. Licensees shall issue no statements, criticisms, or
to Employers and Clients, and (3) Licensee's Obligation to
arguments on engineering and surveying matters that
Other Licensees. The principles amplified in these sections
are inspired or paid for by interested parties, unless they
are important guides to appropriate behavior of professional
explicitly identify the interested parties on whose behalf
engineers.
they are speaking and reveal any interest they have in
Application of the code in many situations is not controversial. the matters.
However, there may be situations in which applying the code 7. Licensees shall not partner, practice, or offer to practice
may raise more difficult issues. In particular, there may be with any person or firm that they know is engaged
circumstances in which terminology in the code is not clearly in fraudulent or dishonest business or professional
defined, or in which two sections of the code may be in conflict. practices.
For example, what constitutes "valuable consideration" or 8. Licensees who have knowledge or reason to believe
"adequate" knowledge may be interpreted differently by that any person or firm has violated any rules or laws
qualified professionals. These types of questions are called applying to the practice of engineering or surveying
conceptual issues, in which definitions of terms may be in shall report it to the board, may report it to appropriate
dispute. In other situations, factual issues may also affect ethical legal authorities, and shall cooperate with the board and
dilemmas. Many decisions regarding engineering design may be those authorities as may be requested.
based upon interpretation of disputed or incomplete information. 9. Licensees shall not knowingly provide false or
In addition, tradeoffs revolving around competing issues of risk incomplete information regarding an applicant in
vs. benefit, or safety vs. economics may require judgments that obtaining licensure.
are not fully addressed simply by application of the code.
3 ETHICS
10. Licensees shall comply with the licensing laws and C. Licensee's Obligation to Other Licensees
rules governing their professional practice in each of the 1. Licensees shall not falsify or permit misrepresentation
jurisdictions in which they practice. of their, or their associates', academic or professional
qualifications. They shall not misrepresent or
B. Licensee's Obligation to Employer and Clients
exaggerate their degree of responsibility in prior
1. Licensees shall undertake assignments only when
assignments nor the complexity of said assignments.
qualified by education or experience in the specific
Presentations incidental to the solicitation of
technical fields of engineering or surveying involved.
employment or business shall not misrepresent pertinent
2. Licensees shall not affix their signatures or seals to
facts concerning employers, employees, associates,
any plans or documents dealing with subject matter in
joint ventures, or past accomplishments.
which they lack competence, nor to any such plan or
2. Licensees shall not offer, give, solicit, or receive, either
document not prepared under their responsible charge.
directly or indirectly, any commission, or gift, or other
3. Licensees may accept assignments and assume
valuable consideration in order to secure work, and
responsibility for coordination of an entire project,
shall not make any political contribution with the intent
provided that each technical segment is signed and
to influence the award of a contract by public authority.
sealed by the licensee responsible for preparation of that
3. Licensees shall not injure or attempt to injure,
technical segment.
maliciously or falsely, directly or indirectly, the
4. Licensees shall not reveal facts, data, or information
professional reputation, prospects, practice, or
obtained in a professional capacity without the prior
employment of other licensees, nor indiscriminately
consent of the client, employer, or public body on
criticize other licensees' work.
which they serve except as authorized or required by
4. Licensees shall make a reasonable effort to inform
law or rules.
another licensee whose work is believed to contain a
5. Licensees shall not solicit or accept gratuities, directly
material discrepancy, error, or omission that may impact
or indirectly, from contractors, their agents, or other
the health, safety, or welfare of the public, unless such
parties in connection with work for employers or
reporting is legally prohibited.
clients.
6. Licensees shall disclose to their employers or
clients all known or potential conflicts of interest or
other circumstances that could influence or appear
to influence their judgment or the quality of their
professional service or engagement.
7. Licensees shall not accept compensation, financial
or otherwise, from more than one party for services
pertaining to the same project, unless the circumstances
are fully disclosed and agreed to in writing by all
interested parties.
8. Licensees shall not solicit or accept a professional
contract from a governmental body on which a
principal or officer of their organization serves as a
member. Conversely, licensees serving as members,
advisors, or employees of a government body or
department, who are the principals or employees of a
private concern, shall not participate in decisions with
respect to professional services offered or provided by
said concern to the governmental body that they serve.
(Section 150, Disciplinary Action, NCEES Model Law)
9. Licensees shall not use confidential information
received in the course of their assignments as a means
of making personal profit without the consent of the
party from whom the information was obtained.
4 ETHICS
